Invasion percolation is a model that was originally proposed to describe growing networks of fractures. Here we describe a loopless algorithm on random lattices, coupled with an avalanche-based model for bursts. The model reproduces the characteristic $b$-value seismicity and spatial distribution of bursts consistent with earthquakes resulting from hydraulic fracturing (“fracking”). We test models for both site invasion percolation and bond invasion percolation. These have differences on the scale of site and bond lengths $l$. But since the networks are characterized by their large-scale behavior, $l\ll L$, we find small differences between scaling exponents. Though data may not differentiate between models, our results suggest that both models belong to different universality classes.

中文翻译：

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水力压裂无环侵入渗流模型和渗流雪崩破裂模型的通用性类

侵入渗流是最初提出来描述不断增长的裂缝网络的模型。在这里，我们描述了随机晶格上的无环算法，以及基于雪崩的突发模型。模型再现特性$b$水力压裂（“压裂”）引起的地震，具有一定的地震活动价值和爆发性空间分布。我们测试站点入侵渗透和债券入侵渗透的模型。这些在位点规模和键长上有差异$升$。但是由于网络具有大规模行为的特点，$升\ll \mathrm{大号}$，我们发现缩放指数之间的微小差异。尽管数据可能无法区分模型，但我们的结果表明这两个模型属于不同的通用性类别。